On Estimates of Biharmonic Functions on Lipschitz and Convex Domains

2005/10/03 by Zhongwei Shen, Shen, Zhongwei
Mathematics · #35J40 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J40

paper · pdf · doi:10.48550/arxiv.math/0510053

arxiv created 2005/10/03 · arxiv updated 2009/12/01

Abstract

Using Maz'ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in Rⁿ. For n≥ 8, combined with a result in \citeS2, these estimates lead to the solvability of the L^p Dirichlet problem for the biharmonic equation on Lipschitz domains for a new range of p. In the case of convex domains, the estimates allow us to show that the L^p Dirichlet problem is uniquely solvable for any 2-\e<p<∞ and n≥ 4.

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